Intersection Cohomology

Author : Armand Borel
Publisher : Springer Science & Business Media
Page : 243 pages
File Size : 46,8 Mb
Release : 2009-05-21
Category : Mathematics
ISBN : 9780817647650

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Intersection Cohomology by Armand Borel Pdf

This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983. This volume supplies an introduction to the piecewise linear and sheaf-theoretic versions of that theory as developed by M. Goresky and R. MacPherson in Topology 19 (1980), and in Inventiones Mathematicae 72 (1983). Some familiarity with algebraic topology and sheaf theory is assumed.

Author : Frances Kirwan,Jonathan Woolf
Publisher : CRC Press
Page : 250 pages
File Size : 45,6 Mb
Release : 2006-06-07
Category : Mathematics
ISBN : 1584881844

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An Introduction to Intersection Homology Theory, Second Edition by Frances Kirwan,Jonathan Woolf Pdf

Now more that a quarter of a century old, intersection homology theory has proven to be a powerful tool in the study of the topology of singular spaces, with deep links to many other areas of mathematics, including combinatorics, differential equations, group representations, and number theory. Like its predecessor, An Introduction to Intersection Homology Theory, Second Edition introduces the power and beauty of intersection homology, explaining the main ideas and omitting, or merely sketching, the difficult proofs. It treats both the basics of the subject and a wide range of applications, providing lucid overviews of highly technical areas that make the subject accessible and prepare readers for more advanced work in the area. This second edition contains entirely new chapters introducing the theory of Witt spaces, perverse sheaves, and the combinatorial intersection cohomology of fans. Intersection homology is a large and growing subject that touches on many aspects of topology, geometry, and algebra. With its clear explanations of the main ideas, this book builds the confidence needed to tackle more specialist, technical texts and provides a framework within which to place them.

Author : David Chataur,Martintxo Saralegi-Aranguren,Daniel Tanré
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 42,8 Mb
Release : 2018-08-09
Category : Electronic
ISBN : 9781470428877

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Intersection Cohomology, Simplicial Blow-Up and Rational Homotopy by David Chataur,Martintxo Saralegi-Aranguren,Daniel Tanré Pdf

Let X be a pseudomanifold. In this text, the authors use a simplicial blow-up to define a cochain complex whose cohomology with coefficients in a field, is isomorphic to the intersection cohomology of X, introduced by M. Goresky and R. MacPherson. The authors do it simplicially in the setting of a filtered version of face sets, also called simplicial sets without degeneracies, in the sense of C. P. Rourke and B. J. Sanderson. They define perverse local systems over filtered face sets and intersection cohomology with coefficients in a perverse local system. In particular, as announced above when X is a pseudomanifold, the authors get a perverse local system of cochains quasi-isomorphic to the intersection cochains of Goresky and MacPherson, over a field. We show also that these two complexes of cochains are quasi-isomorphic to a filtered version of Sullivan's differential forms over the field Q. In a second step, they use these forms to extend Sullivan's presentation of rational homotopy type to intersection cohomology.

Author : Laurenţiu G. Maxim
Publisher : Springer Nature
Page : 270 pages
File Size : 43,7 Mb
Release : 2019-11-30
Category : Mathematics
ISBN : 9783030276447

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Intersection Homology & Perverse Sheaves by Laurenţiu G. Maxim Pdf

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson–Bernstein–Deligne–Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito’s deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

Author : Enrique Macias-virgos,Jesus A Alvarez Lopez,Xose Masa
Publisher : World Scientific
Page : 258 pages
File Size : 51,9 Mb
Release : 1995-11-17
Category : Electronic
ISBN : 9789814549615

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Analysis And Geometry In Foliated Manifolds - Proceedings Of The 7th International Colloquium On Differential Geometry by Enrique Macias-virgos,Jesus A Alvarez Lopez,Xose Masa Pdf

The subject of this volume, recent developments in foliation theory and important related analytic and geometric techniques, is an active field in the application of both global analysis and geometric topological theory of manifolds to the study of foliations. This volume includes research papers by leading specialists, giving an overview of this subject.

Author : José Luis Cisneros-Molina,Dũng Tráng Lê,José Seade
Publisher : Springer Nature
Page : 581 pages
File Size : 42,6 Mb
Release : 2021-11-01
Category : Mathematics
ISBN : 9783030780241

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Handbook of Geometry and Topology of Singularities II by José Luis Cisneros-Molina,Dũng Tráng Lê,José Seade Pdf

This is the second volume of the Handbook of the Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory and related topics. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Author : Jérôme Scherer
Publisher : American Mathematical Soc.
Page : 308 pages
File Size : 53,8 Mb
Release : 2018-05-30
Category : Algebraic topology
ISBN : 9781470429119

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An Alpine Bouquet of Algebraic Topology by Jérôme Scherer Pdf

This volume contains the proceedings of the Alpine Algebraic and Applied Topology Conference, held from August 15–21, 2016, in Saas-Almagell, Switzerland. The papers cover a broad range of topics in modern algebraic topology, including the theory of highly structured ring spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic -theory and topological cyclic, periodic, or Hochschild homology, intersection cohomology, and symplectic topology.

Author : A.I. Kostrikin,I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 45,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662032350

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Algebra IX by A.I. Kostrikin,I.R. Shafarevich Pdf

The first contribution by Carter covers the theory of finite groups of Lie type, an important field of current mathematical research. In the second part, Platonov and Yanchevskii survey the structure of finite-dimensional division algebras, including an account of reduced K-theory.

Author : Markus Banagl
Publisher : Springer
Page : 224 pages
File Size : 49,5 Mb
Release : 2010-06-16
Category : Mathematics
ISBN : 9783642125898

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Intersection Spaces, Spatial Homology Truncation, and String Theory by Markus Banagl Pdf

Intersection cohomology assigns groups which satisfy a generalized form of Poincaré duality over the rationals to a stratified singular space. This monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality. The cornerstone of the method is a process of spatial homology truncation, whose functoriality properties are analyzed in detail. The material on truncation is autonomous and may be of independent interest tohomotopy theorists. The cohomology of intersection spaces is not isomorphic to intersection cohomology and possesses algebraic features such as perversity-internal cup-products and cohomology operations that are not generally available for intersection cohomology. A mirror-symmetric interpretation, as well as applications to string theory concerning massless D-branes arising in type IIB theory during a Calabi-Yau conifold transition, are discussed.

Author : Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun
Publisher : American Mathematical Soc.
Page : 436 pages
File Size : 51,7 Mb
Release : 2017-12-15
Category : Algebraic varieties
ISBN : 9781470435745

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Geometry of Moduli Spaces and Representation Theory by Roman Bezrukavnikov,Alexander Braverman,Zhiwei Yun Pdf

This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan–Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry. Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections. The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions.

Author : Workshop on Topology,Steven Hurder
Publisher : American Mathematical Soc.
Page : 287 pages
File Size : 45,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851708

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Differential Topology, Foliations, and Group Actions by Workshop on Topology,Steven Hurder Pdf

This volume contains the proceedings of the Workshop on Topology held at the Pontificia Universidade Catolica in Rio de Janeiro in January 1992. Bringing together about one hundred mathematicians from Brazil and around the world, the workshop covered a variety of topics in differential and algebraic topology, including group actions, foliations, low-dimensional topology, and connections to differential geometry. The main concentration was on foliation theory, but there was a lively exchange on other current topics in topology. The volume contains an excellent list of open problems in foliation research, prepared with the participation of some of the top world experts in this area. Also presented here are two surveys on group actions---finite group actions and rigidity theory for Anosov actions---as well as an elementary survey of Thurston's geometric topology in dimensions 2 and 3 that would be accessible to advanced undergraduates and graduate students.

Author : Greg Friedman
Publisher : Cambridge University Press
Page : 491 pages
File Size : 44,5 Mb
Release : 2011-03-28
Category : Mathematics
ISBN : 9780521191678

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Topology of Stratified Spaces by Greg Friedman Pdf

This book explores the study of singular spaces using techniques from areas within geometry and topology and the interactions among them.

Author : Greg Friedman
Publisher : Cambridge University Press
Page : 823 pages
File Size : 40,5 Mb
Release : 2020-09-24
Category : Mathematics
ISBN : 9781107150744

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Singular Intersection Homology by Greg Friedman Pdf

The first expository book-length introduction to intersection homology from the viewpoint of singular and piecewise linear chains.

Author : Frances Clare Kirwan
Publisher : Halsted Press
Page : 169 pages
File Size : 44,7 Mb
Release : 1988
Category : Algebra, Homological
ISBN : 0470211989

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An Introduction to Intersection Homology Theory by Frances Clare Kirwan Pdf

Author : David Mumford,John Fogarty,Frances Kirwan
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 43,9 Mb
Release : 1994
Category : Mathematics
ISBN : 3540569634

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Geometric Invariant Theory by David Mumford,John Fogarty,Frances Kirwan Pdf

"Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.